in_sphere.hpp File Reference

Consists of methods that test whether a given query point is inside the unique sphere circumscribing a 2D triangle or a 3D tetrahedron. More...

#include "axom/core.hpp"
#include "axom/primal/geometry/Point.hpp"
#include "axom/primal/geometry/Triangle.hpp"
#include "axom/primal/geometry/Tetrahedron.hpp"
#include "axom/primal/geometry/OrientationResult.hpp"
#include "axom/primal/operators/detail/predicate_determinants.hpp"

Namespaces
	axom
	axom::primal

Functions
template<typename T >
double	axom::primal::in_sphere_determinant (const Point< T, 2 > &q, const Point< T, 2 > &p0, const Point< T, 2 > &p1, const Point< T, 2 > &p2)
	Returns the raw 2D in-sphere determinant for a circumcircle test. More...
template<typename T >
double	axom::primal::in_sphere_determinant (const Point< T, 2 > &q, const Triangle< T, 2 > &tri)
template<typename T >
double	axom::primal::in_sphere_determinant (const Point< T, 3 > &q, const Point< T, 3 > &p0, const Point< T, 3 > &p1, const Point< T, 3 > &p2, const Point< T, 3 > &p3)
	Returns the raw 3D in-sphere determinant for a circumsphere test. More...
template<typename T >
double	axom::primal::in_sphere_determinant (const Point< T, 3 > &q, const Tetrahedron< T, 3 > &tet)
template<typename T >
int	axom::primal::in_sphere_orientation (const Point< T, 2 > &q, const Point< T, 2 > &p0, const Point< T, 2 > &p1, const Point< T, 2 > &p2, double EPS=1e-8)
	Classifies a query point against a 2D triangle's circumcircle. More...
template<typename T >
int	axom::primal::in_sphere_orientation (const Point< T, 2 > &q, const Triangle< T, 2 > &tri, double EPS=1e-8)
template<typename T >
int	axom::primal::in_sphere_orientation (const Point< T, 3 > &q, const Point< T, 3 > &p0, const Point< T, 3 > &p1, const Point< T, 3 > &p2, const Point< T, 3 > &p3, double EPS=1e-8)
	Classifies a query point against a 3D tetrahedron's circumsphere. More...
template<typename T >
int	axom::primal::in_sphere_orientation (const Point< T, 3 > &q, const Tetrahedron< T, 3 > &tet, double EPS=1e-8)
template<typename T >
bool	axom::primal::in_sphere (const Point< T, 2 > &q, const Point< T, 2 > &p0, const Point< T, 2 > &p1, const Point< T, 2 > &p2, double EPS=1e-8, bool includeBoundary=false)
	Tests whether a query point lies inside a 2D triangle's circumcircle. More...
template<typename T >
bool	axom::primal::in_sphere (const Point< T, 2 > &q, const Triangle< T, 2 > &tri, double EPS=1e-8, bool includeBoundary=false)
	Tests whether a query point lies inside a 2D triangle's circumcircle. More...
template<typename T >
bool	axom::primal::in_sphere (const Point< T, 3 > &q, const Point< T, 3 > &p0, const Point< T, 3 > &p1, const Point< T, 3 > &p2, const Point< T, 3 > &p3, double EPS=1e-8, bool includeBoundary=false)
	Tests whether a query point lies inside a 3D tetrahedron's circumsphere. More...
template<typename T >
bool	axom::primal::in_sphere (const Point< T, 3 > &q, const Tetrahedron< T, 3 > &tet, double EPS=1e-8, bool includeBoundary=false)
	Tests whether a query point lies inside a 3D tetrahedron's circumsphere. More...
template<typename T >
bool	axom::primal::in_sphere (const BoundingBox< T, 2 > &bb, const Sphere< T, 2 > &circle)
	Tests whether a bounding box lies inside a 2D sphere. More...

Detailed Description

Consists of methods that test whether a given query point is inside the unique sphere circumscribing a 2D triangle or a 3D tetrahedron.

This is a well known computational geometry primitive. For reference, see Section 3.1.6.4 in "Real-time collision detection" by C. Ericson.

Note

These routines use double-precision determinants and are not exact sign oracles near degeneracy (e.g. nearly co-circular/co-spherical inputs). See detail/predicate_determinants.hpp for the precision/robustness discussion and in_sphere_orientation() for the tolerance (EPS) scaling caveat.